Solve for $x$ and $y$ using elimination. ${6x+3y = 39}$ ${-5x-3y = -37}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $3y$ and $-3y$ cancel out. ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {6x+3y = 39}\thinspace$ to find $y$ ${6}{(2)}{ + 3y = 39}$ $12+3y = 39$ $12{-12} + 3y = 39{-12}$ $3y = 27$ $\dfrac{3y}{{3}} = \dfrac{27}{{3}}$ ${y = 9}$ You can also plug ${x = 2}$ into $\thinspace {-5x-3y = -37}\thinspace$ and get the same answer for $y$ : ${-5}{(2)}{ - 3y = -37}$ ${y = 9}$